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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2301.06109 |
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| _version_ | 1866910521821757440 |
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| author | Quattropani, Matteo |
| author_facet | Quattropani, Matteo |
| contents | We consider a version of the classical Ehrenfest urn model with two urns and two types of balls: regular and heavy. Each ball is selected independently according to a Poisson process having rate $1$ for regular balls and rate $α\in(0,1)$ for heavy balls, and once a ball is selected, is placed in a urn uniformly at random. We study the asymptotic behavior when the total number of balls, $N$, goes to infinity, and the number of heavy ball is set to $m_N\in\{1,\dots, N-1\}$. We focus on the observable given by the total number of balls in the left urn, which converges to a binomial distribution of parameter $1/2$, regardless of the choice of the two parameters, $α$ and $m_N$. We study the speed of convergence and show that this can exhibit three different phenomenologies depending on the choice of the two parameters of the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_06109 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mixing trichotomy for an Ehrenfest urn with impurities Quattropani, Matteo Probability We consider a version of the classical Ehrenfest urn model with two urns and two types of balls: regular and heavy. Each ball is selected independently according to a Poisson process having rate $1$ for regular balls and rate $α\in(0,1)$ for heavy balls, and once a ball is selected, is placed in a urn uniformly at random. We study the asymptotic behavior when the total number of balls, $N$, goes to infinity, and the number of heavy ball is set to $m_N\in\{1,\dots, N-1\}$. We focus on the observable given by the total number of balls in the left urn, which converges to a binomial distribution of parameter $1/2$, regardless of the choice of the two parameters, $α$ and $m_N$. We study the speed of convergence and show that this can exhibit three different phenomenologies depending on the choice of the two parameters of the model. |
| title | Mixing trichotomy for an Ehrenfest urn with impurities |
| topic | Probability |
| url | https://arxiv.org/abs/2301.06109 |